The propagation of a radio wave through a very great thickness of weakly scattering medium is studied. An important application is to the interplanetary scintillation of a radio star of finite angular diameter observed with a receiver of finite bandwidth. A previous paper gave the theory and results for a medium whose irregularities are so weak that only single scatter is important. It is now extended to deal with multiple scatter. A partial differential equation is formulated and a series solution is derived which converges when the receiver is in the 'near field' for the whole of the scattering medium. A few typical results are given for the scintillation index, scintillation visibility and spatial autocorrelation function of the fluctuations of received intensity, for some particular cases of source brightness function, receiver band-pass function and autocorrelation function of the irregularities in the medium.